The Determinants of Nuclear Force Structure*
Erik Gartzke†
Jeffrey M. Kaplow
Rupal N. Mehta
*
The authors thank Matthew Kroenig, Bryan Early, Dave Ohls, Rebecca Sanders, Adam Stulberg, two anonymous
reviewers, and the other authors in this special issue for valuable comments. Earlier versions of this paper were
presented at the 2012 Midwest Political Science Association Annual Conference and the 2012 International Studies
Association Annual Convention.
†
University of California, San Diego, Department of Political Science, 9500 Gilman Ave. #0521, La Jolla, CA
92037. E-mail: [email protected]; [email protected]; [email protected].
1
The Determinants of Nuclear Force Structure
Abstract:
A substantial literature examines the causes of nuclear proliferation, but few studies have
addressed why states decide on a particular portfolio of weapons systems once they have
acquired a basic nuclear capability. We advance a portfolio theory of nuclear force structure,
positing that states seek a diverse set of capabilities for nuclear deterrence, but that they also face
major resource and organizational constraints. A number of factors may help to explain the
portfolio of nuclear forces that states ultimately field, including resource availability, experience
as a nuclear power, bureaucratic politics, the conventional threat environment, the presence of
nuclear rivals, and the maintenance of nuclear alliances. We test the influence of these factors on
force structure using a new dataset of nuclear weapons platforms fielded by nine nuclear nations
between 1950 and 2000. Our findings represent an important step in understanding the drivers of
nuclear behavior after states have joined the nuclear weapons club.
Word Count: 10,985
2
Introduction
States that have acquired nuclear weapons must confront the complicated and important question
of how to structure their nuclear arsenals.i Some states, such as the United Kingdom, field only a
small number of nuclear platforms while others, such as the United States and the Soviet Union,
establish diverse portfolios of weapons with varying range, destructive power, and other
characteristics.ii Nuclear states differ dramatically not only in the number of nuclear platforms
they deploy, but also in the relative weight they place on particular weapons systems and on each
component of the nuclear triad (air, land, and sea-based weapons).iii These characteristics have
also changed over time—nuclear forces that seem appropriate in one strategic environment may
be made redundant or obsolete by the introduction of new technologies or by cycles of crisis and
détente. Variation across nations and time raises several key questions: Why do states deploy
the nuclear force structures they do? What drives the decisions of states to invest in new nuclear
platforms? How do officials think about the diversification of their nuclear portfolios?
The answers to these questions are important both theoretically and in practice. The
diversification of nuclear forces is intimately tied to conceptions of nuclear deterrence, secure
second-strike capability, and mutually assured destruction. A particular force structure may be
more or less vulnerable to pre-emptive attack, more or less effective at targeting opposing forces,
and more or less capable of mobilizing quickly in the event of crisis. It has long been believed,
for example, that fielding a diverse set of platforms covering each leg of the nuclear triad reduces
vulnerability to sudden attack, even as it increases the flexibility of possible responses. If force
structure is indeed an important element of deterrence effectiveness, then the determinants of a
state’s nuclear forces may mean the difference between sustained peace and a nuclear crisis.
3
Nuclear force structure is not just a relic of Cold War thinking. There remains a lively
policy debate about the role of nuclear forces in an era of US nuclear supremacy (Flory 2006;
Lieber and Press 2006, 2009; Payne 2006). Force structure has also played an important role in
policy discussions surrounding the New START treaty (Pifer 2010), calls for the move toward
“Global Zero” in which the number of nuclear weapons is dramatically reduced or eliminated
(Cortright and Väyrynen 2010; U.S. Department of Defense 2010), and ongoing work to ensure
the reliability of the US nuclear deterrent into the future (Chyba and Crouch 2009). India and
Pakistan also grapple with how their nuclear postures affect deterrence in a context very different
from the Cold War stand-off between the United States and Soviet Union (Narang 2010).
Despite the obvious relevance of these issues, academic research on nuclear arsenals has
primarily sought to explain horizontal proliferation and the effect of a larger number of nuclear
weapons states on the international system. Here, we attempt to remedy this situation by
considering both the theoretical and empirical determinants of nuclear force structure. We
proceed in five parts. First, we briefly review existing studies of nuclear proliferation and force
structure. Second, we present a theoretical framework in which to understand the various factors
that might influence the nuclear force structure decisions of states. Third, we introduce an
original dataset compiled for this analysis and present several quantitative models of nuclear
force structure. We report our findings in section four. Finally we conclude with suggestions for
future research into the dynamics of nuclear force structure decisions.
Existing Approaches
Most studies of nuclear proliferation address why and how states build or acquire initial nuclear
capabilities (Jo and Gartzke 2007; Sagan 1996; Singh and Way 2004; Solingen 1994), or the
effect of proliferation on international security (Asal and Beardsley 2007; Beardsley and Asal
4
2009; Gartzke and Jo 2009; Sagan and Waltz 1995). These studies provide a broad framework
for understanding the causes and consequences of horizontal proliferation. A recent wave of
quantitative work has built on this framework, focusing on one or two specific factors that lead
states to seek nuclear capabilities (Gartzke and Kroenig, this issue). This work emphasizes both
supply-side factors, including access to external nuclear assistance (Brown and Kaplow, this
issue; Fuhrmann 2009; Kroenig 2009), and the demand-side, such as defense pacts with nuclear
states, the forward deployment of weapons, or the availability of alternative weapons of mass
destruction (Bleek and Lorber, this issue; Horowitz and Narang, this issue; Sechser and
Fuhrmann, this issue). Some scholars have sought to link nuclear force structure decisions of
existing nuclear states to decisions by other states to proliferate (Tago and Singer 2011), but little
recent work addresses the determinants of vertical proliferation itself.
An established literature on organizational dynamics and bureaucratic politics, much of it
written in the context of the Cold War superpower rivalry, offers one approach to understanding
nuclear force structure. Authors in this tradition argue that militaries, like other organizations,
have a preference for the status quo; any push for adaptation or change is generally resisted by
entrenched interests (Allison and Morris 1975; Halperin 1974; Perrow 1986; Sagan 1994; Waltz
1990). Given that technological change and the introduction of new missions or weapons can
threaten the status quo, military organizations have incentives to delay these developments and
instead protect the existing distribution of resources and power (Halperin 1974; Sagan 1996).
Evidence for bureaucratic inertia can be gleaned from incidents such as the introduction
of second-strike survivable forces in the United States, which only came about after significant
pressure from civilian authorities. US naval leaders opposed introduction of submarine-launched
ballistic missile (SLBM) systems, for example. According to Sapolsky, “the major impediment
5
to development of the Polaris missile system was the Navy’s indecisiveness about sponsoring a
ballistic missile program” (Sapolsky 1972). Given the Eisenhower administration’s projected
budget cuts, senior naval officials were concerned that the new class of naval nuclear weapons
would threaten the maintenance of forces central to the Navy’s traditional missions.
Another literature points to arms racing as an explanation for nuclear forces. Richardson
(1960) argued that “fear of opponent’s weapons and capability generally, without an agreement,
would lead to an arms race to ensure stable deterrence.” According to this perspective, fear of
enemy nuclear capabilities and the push for an effective deterrent against any rival state
precipitates development of an offensive strategic nuclear force. Alain Enthoven, an aide to
Robert McNamara, summarized the ‘official position’ of the superpowers: “it is important to
understand this iteration of opposing strategic forces and its relation to the strategic force
planning process. If the overriding objective of our strategic nuclear force is to deter a first strike
against us, the United States must have a second-strike capability. This action-reaction
phenomenon is central to all strategic force planning issues as well as to any theory of an arms
race” (Enthoven and Smith 1971; Kugler et. al.1980).
This arms racing explanation extends beyond the US-Soviet rivalry to describe the tense
relationship between India and Pakistan. According to Chari (2001), the need for a triad to
establish a survivable nuclear force, and subsequent inter-service rivalry, accelerated South
Asian tensions. Narang (2010) sees nuclear force structure in the context of the nuclear postures
both states employ in order to effectively deter their rival.
Still another body of work addresses the causes and consequences of conventional force
modernization, military technology development, and the acquisition of new capabilities such as
ballistic missiles (Barkley 2008; Bas and Coe 2012; Eyre and Suchman 1996; Mettler and Reiter
6
2012; Rosen 1991; Sechser and Saunders 2010). Sechser and Saunders (2010), for example, find
that the mechanization of a state’s military depends more on its security environment than it does
on its domestic institutions. Mettler and Reiter (2012) and Barkley (2008) find similarly that the
presence of ballistic missiles in a neighboring state is a significant driver of a country’s decision
to acquire missile technology. Because nuclear forces piggyback on conventional capabilities—
aircraft, submarines, and missile technology—there is likely to be some overlap between the
determinants of conventional military modernization and those of nuclear force structure.
While the bureaucratic politics and conventional arm racing literatures introduce
important ideas about the drivers of nuclear force structure, this work often focuses on single
case studies and rarely tests these theories in a systematic way. By focusing mainly on a small
number of cases, existing research may also miss some important tradeoffs that states must face
in fielding an entire arsenal of nuclear weapons systems. In the next section, we advance a
portfolio theory of nuclear force structure that seeks to fill the gap between existing analytical
conceptions.
A Portfolio Theory of Nuclear Force Structure
Policymakers may have numerous goals in mind when making decisions about nuclear force
structures. States, for example, may seek out particular capabilities through the acquisition of
individual nuclear platforms. Nuclear platforms vary in terms of range, destructive power,
vulnerability to attack, effectiveness against different kinds of enemy forces, and other important
attributes. The capability of an individual nuclear platform, however, is not the whole story. If a
given weapon system dominated all others on every metric, nuclear arsenals might emphasize a
single delivery vehicle. In reality, states must consider the totality of their nuclear capabilities,
and so look to diversify arsenals, creating a portfolio of platforms that best achieves state goals.
7
Diversification is advantageous for defensive reasons. Lacking experience with nuclear
conflict, nations cannot know which weapons will prove most effective or most vulnerable on
the battlefield. Emphasizing a particular nuclear platform increases the risk that the weapons
system will become vulnerable to enemy counter-force targeting or other measures, or even to
unforeseen or accidental logistical or maintenance problems (Sagan 1993). This is one of the
fundamental justifications for the nuclear triad. According to former Secretary of the Air Force
Thomas Reed, “Its diversity poses an insoluble targeting problem to any aggressor. Any attack
that might seriously cripple one leg of the Triad constitutes a clear and unambiguous warning to
the other two. There is no known way to attack all three simultaneously” (McCarthy 1976).
Diversification may also hold benefits for the offense, by facilitating attacks on a range of
different enemy forces and by complicating the challenge faced by an opponent seeking to limit
its vulnerability (Burt 1978; McCarthy 1976; Snow 1979). Diversification allows one weapons
system to compensate for weaknesses in another. Strategic bombers, for example, while more
flexible and dispersed than ICBMs, are vulnerable to air defenses in a way that missile systems
are not. Submarine-launched systems, in turn, are more difficult for an adversary to hold at risk,
but pose additional challenges for command and control. By fielding weapons systems of
different types, states also demand more from an opponent trying to defend against attack. This
is a significant advantage of diversification; an adversary may decline to invest in air defense, for
example, knowing that a state can also bring missile systems to bear. The presence of the missile
system, then, may actually increase the potential offensive power of air assets in the portfolio.
Diversification inoculates offensive capabilities against potentially disruptive defensive
technologies. New advances in missile defense systems, for example, are less worrying if a state
also fields strategic air assets. Diversified nuclear portfolios further hedge against unanticipated
8
changes in the strategic environment. The weapon system best able to hold a fading adversary at
risk might be less effective in deterring the next rising opponent. Having forces of different
types and capabilities minimizes the risk that a nuclear portfolio will become obsolete.
Of course, portfolio diversification is costly. The development of nuclear platforms with
unique capabilities calls for economic and technical resources that may be in short supply. These
costs may go beyond those associated with developing a different type of missile; platforms are
often designed specifically for a particular physics package—the nuclear component of the
overall weapon—and the costs of fielding new nuclear weapons designs can be substantial. New
nuclear platforms also carry significant opportunity costs. Investments in nuclear development
may displace funding for conventional military weapons, as well as other national priorities.
Some kinds of diversification may simply be beyond a state’s technical capabilities, or
may require military or civilian infrastructure that a state does not possess. SLBMs, for example,
require a submarine and extensive naval infrastructure. Limited naval capabilities may help to
explain a state’s decision not to develop submarine-launched nuclear platforms. Long-range
missile systems pose their own technical challenges, and the difficulty of mastering missile
technology may limit the extent to which a state can diversify its nuclear portfolio.
Finally, diversification may have significant consequences when it comes to the structure
of military organizations and a nation’s command and control capability. Military organizations
may resist nuclear weapons if commanders see them as distracting from their traditional mission,
or they may covet nuclear weapons as a signal of prestige and organizational power (Sagan
1996). In either case, extending nuclear weapons to a different branch of the military (as states
are forced to do, for example, when they first deploy SLBMs) is potentially fraught with political
complications. Diversification also places additional stress on nuclear command and control
9
mechanisms. Ensuring effective government control of nuclear weapons and guarding against
unauthorized or accidental use is challenging enough when all nuclear weapons are tightly held
within a single military organization. Dispersing weapons across organizational boundaries
makes it more difficult to maintain positive control and targeting (Kak 1998; Younger 2000).
There are several ways to explain the structure of nuclear forces, given the advantages
and disadvantages of a diversified nuclear portfolio. These explanations can be organized as
domestic constraints, bureaucratic politics, conventional threats, nuclear rivalries, and nuclear
alliances.
Domestic Constraints
One of the most basic determinants of the diversification of a state’s nuclear force structure may
be the state’s underlying capacity. States that lack advanced technology face additional hurdles
in developing nuclear ballistic missiles, while states without submarines cannot field SLBMs.
Capacity limitations that inhibit the development of new military capabilities are likely also to
limit the diversity of nuclear forces. Such constraints may be a function of the economic
strength of the state, or states may lack the resources or expertise necessary to miniaturize and
mass-produce the sophisticated nuclear physics packages that can be mated to advanced weapons
platforms. Specific weapons systems also require infrastructure that may not be available—from
advanced command and control mechanisms to a trained officer corps. Military resources place
critical limits on how diverse nuclear force structures can become.
10
Resources Hypothesis: Diversification of nuclear forces should increase with greater
levels of economic, technical, and military resources.
These kinds of capacity limitations point to another potential driver of diversified nuclear
forces: the passage of time. Several aspects of nuclear force structure, such as necessary military
infrastructure or nuclear design expertise, develop over time. Even conventionally sophisticated
states are unlikely to be fully ready for a diversified nuclear portfolio from the moment that they
enter the nuclear club. It may be that nuclear states follow a common trajectory; for example,
they may initially press conventional forces into service as nuclear delivery vehicles (typically
heavy bombers and attack aircraft) before slowly developing a more diverse set of nuclear
platforms. States may eventually reach a kind of force structure equilibrium at nuclear maturity,
in which new forces are deployed only to replace aging and obsolete forces of equivalent type.
Evolving nuclear force structures may reflect more than just the passage of time, however.
States may also gain experience with nuclear weapons, learning to manage nuclear deterrence.
Deterrence is more effective if forces are less vulnerable to attack, and when the promise of a
retaliatory counterstrike is most credible. Part of the learning process for nuclear states might
involve adopting nuclear force structures that are more adept at deterring aggression. Horowitz
(2009) finds that new nuclear weapons states are more conflict prone, but that over time nuclear
weapons states become less likely to engage in disputes than states without nuclear weapons.
One possible explanation for this result is that states adjust to their newfound nuclear status by
diversifying their nuclear forces, to more effectively deter external aggressors.iv
Maturity Hypothesis: Diversification of nuclear forces should increase as a state gains
experience with nuclear weapons.
11
Bureaucratic Politics
The decision to diversify nuclear forces may be imposed on the military from civilian leaders or
other government officials. The extant literature argues that militaries, like other organizations,
have a preference for the status quo. Military organizations have an incentive not to pursue new
missions and technologies, and instead to protect the existing distribution of resources and power.
In short, stronger military organizations are likely to present obstacles to the timely
diversification of nuclear portfolios.
Bureaucratic Politics Hypothesis: Diversification of nuclear forces should decrease as a
military bureaucracy grows stronger.
Conventional Threats
Scholarship on the determinants of nuclear proliferation indicates that when states feel threatened,
even by conventional forces, they are more likely to develop nuclear weapons (Singh and Way
2004; Jo and Gartzke 2007). Conventional threats may also have an effect on states’ decisions to
diversify their nuclear portfolios. The ultimate direction of this effect, however, is unclear.
On one hand, states facing greater conventional threats may seek more diversified nuclear
portfolios to augment their conventional deterrent. Nuclear weapons loom in the background of
any contest with a nuclear state, and a more diverse nuclear force posture may make potential
aggressors less willing to test the credibility of the implicit nuclear threat. NATO commanders,
for example, argued during the Cold War that a secure second-strike capability was essential for
both conventional and nuclear deterrence of the Warsaw Pact (Lebow and Stein 1995). A more
diversified portfolio may also spill over to conventional military power, strengthening command
and control and channeling resources to military assets that can be used for both conventional
12
and nuclear missions, such as submarines. States in a more threatening environment may choose
to diversify their nuclear portfolios partly to take advantage of these positive externalities.
Conventional Deterrence Hypothesis: Diversification of nuclear force structure should
increase as states face greater conventional threats.
On the other hand, the substantial opportunity costs that attend the development of new
nuclear platforms may dissuade threatened states from investing in a diverse nuclear portfolio.
For a state in a dangerous neighborhood, the cost of a new nuclear missile might be better spent
on conventional military capabilities. This is especially true if nuclear weapons possession does
not make conventional conflict significantly less likely, as some studies have found (Gartzke and
Jo 2009). The presence of substantial conventional threats may thus lead states to prioritize
conventional military improvements over the diversification of their nuclear portfolios.
Opportunity Cost Hypothesis: Diversification of nuclear forces should decrease as states
face greater conventional threats.
Nuclear Rivalries
A state’s decision to pursue a particular distribution of nuclear platforms may be influenced by
the presence of a nuclear rival, and by the configuration of the rival’s forces. A simple arms
racing logic suggests that a state will increase the diversification of its portfolio in response to a
more diversified opponent. Yet if states respond to their adversaries’ force structures, the nature
of that response may be far more complex. Nuclear platforms of different types and capabilities
may be required when an opponent increases the overall size of its nuclear arsenal, for example.
The geographic distance between rivals may also play a critical role in determining force
13
structures. Neighboring rivals can reach each other with any weapons system, while distant
adversaries require a diverse set of nuclear platforms—long-range bombers, submarines,
ICBMs—to hold a rival’s homeland at risk. Finally, a state’s level of diversification may depend
on relations with nuclear rivals. As tensions ease, nuclear forces may target other potential
adversaries or contribute to confidence building in the wake of détente. When the next crisis
mounts, the nuclear portfolio may again shift to weapons that best target an enemy’s forces.
Arms Race Hypothesis: Diversification of nuclear forces should increase with the
presence of a rival, as a rival’s nuclear forces become more diversified, or as a rival’s
nuclear forces increase in capability.
Rival Distance Hypothesis: Diversification of nuclear forces should increase with the
geographic distance of a nuclear rival.
Crisis Hypothesis: Diversification of nuclear forces should increase as disputes between
two rivals increase.
Arms control treaties figured prominently in the US and Soviet nuclear rivalry. Both the
United States and the Soviet Union altered their arsenal sizes and their portfolio allocation in the
wake of the SALT and START talks. START I barred its signatories from deploying more than
6,000 nuclear warheads atop a total of 1,600 ICBMs, submarine-launched ballistic missiles, and
bombers. These general reductions may have resulted in significant changes in the number of
different weapons systems deployed. New START, ratified in 2010, further limited the number
of deployed and non-deployed ICBM launchers, SLBM launchers, and heavy bombers to 800.
This agreement has already yielded a change in projections of the future diversification of the US
14
nuclear portfolio (Collina 2010). While these agreements have complex effects, one significant
outcome of arms control efforts may be a reduction in the number of different nuclear platforms
in the field and a corresponding reduction in the diversification of nuclear portfolios.
Arms Control Hypothesis: Diversification of nuclear forces should decrease in response
to arms control treaties.
Nuclear Alliances
Alliances between nuclear states may drive force structure decisions in opposing ways. First,
states may construct nuclear force structures that complement the nuclear portfolios of their
allies. If states consider the totality of nuclear forces within the alliance, then they should
structure their own forces to mitigate weaknesses in the collective portfolio. If, for example, an
ally boasts a highly concentrated force structure, then the state may seek to diversify, while a
well-equipped ally may alleviate the need for a state to seek diversity in its own forces. In the
latter case, the state may be seen as free riding on the nuclear investments of its ally.
Complements Hypothesis: Diversification of nuclear forces should decrease with the
presence of a nuclear ally, as an ally’s nuclear forces become more diversified, or as an
ally’s nuclear forces increases in capability.
Alternatively, alliance relationships may push states to create nuclear forces in the same
image as their allies. This may reflect a desire to standardize capabilities with alliance partners,
to facilitate economies of scale and improve the interoperability of allied militaries. Duplicating
force structures may also result unintentionally from technology transfer. Allies are more likely
to share weapons technology, causing partners to develop similar weapons systems. If this
15
dynamic holds sway, having an ally that fields a diverse range of nuclear platforms might lead a
state to diversify its forces in comparable ways, even deploying comparable platforms.
If states adjust their force structures to counter rivals, however, then mirror imaging
among the force structures of allies may owe more to the presence of a common adversary than
to alliance dynamics. Faced with similar external threats, it would not be surprising to see allied
states take similar approaches to efficiently and effectively deterring their adversaries.
Mirror Image Hypothesis: Diversification of nuclear forces should increase with the
presence of a nuclear ally, as an ally’s nuclear forces become more diversified, or as an
ally’s nuclear forces increase in capability.
States offering a credible nuclear umbrella must ultimately be capable of coming to the
aid of their allies. The nuclear force structure required to do so may depend, as in the case of
nuclear rivalry, on the ally’s geographic distance. More diversified forces may be necessary to
reach distant allies, while nearly any weapons system could be relevant to a nearby conflict.
Ally Distance Hypothesis: Diversification of nuclear forces should increase with the
geographic distance of a nuclear ally.
Testing the Determinants of Nuclear Force Structure
To analyze the determinants of nuclear force structure, we created a new dataset of nuclear
platforms with annual observations for nine nuclear states between 1950 and 2000.v Data were
obtained from several secondary sources, including the National Resources Defense Council’s
Nuclear Weapons Databook (Cochran, Arkin, and Hoenig 1984; Cochran et al. 1989; Norris,
Burrows, and Fieldhouse 1994), the Air Force Digest, SIPRI’s annual yearbook, and the Military
16
Balance from the International Institute for Strategic Studies (IISS). Country-specific sources
were also consulted.vi
This dataset can help us understand how states develop and maintain a portfolio of
nuclear weapons assets. One important aspect of portfolio maintenance is the development of
different types of nuclear platforms. In their early years, nuclear nations steadily develop a
number of new nuclear-specific platforms to support their nuclear deterrent, but the number of
unique platforms seems to level off as states reach nuclear maturity. Platforms are still being
created, but these are mostly produced to replace existing platforms that are then retired from
service. This trend from adolescent to mature force structure is shown in Figure 1.
The solid black line in Figure 1 represents the average number of unique platforms for all
nuclear weapons states at a given level of nuclear experience.vii The general trend is a slow
increase in the number of unique nuclear platforms from nuclear acquisition to about 30 years of
nuclear experience, when the trend line begins to level off. Fluctuations at just over 40 years of
nuclear experience correspond with US and Russian force structure changes at the end of the
Cold War. The number of unique platforms is contingent, however, on the types of delivery
vehicles the state deploys. The solid gray line in Figure 1 shows the average number of unique
platforms among states that employ only aircraft as delivery vehicles; the dotted line represents
states with both aircraft and land-based missiles, and the dashed gray line represents states with
the full nuclear triad—aircraft, land-based missiles, and SLBMs.viii As expected, triad states rely
on more unique platforms than states with just missiles and aircraft or with missiles alone.
[Figure 1 about here]
Nuclear portfolios seem to become more diversified with nuclear experience and with the
development of new weapons systems, but there is still substantial variation within each category.
17
This can be seen from the vertical lines in Figure 1 representing the range of platforms available
to nuclear weapons states at that level of nuclear experience. To better understand this variation,
we offer several statistical models of nuclear portfolio diversification, testing a number of factors
behind a state’s nuclear force structure decisions. In the remainder of this section, we describe
the elements of our statistical model. Table 1 presents a summary of the hypotheses derived in
the previous section, their predicted effect, and the explanatory variables used to test them.
[Table 1 about here]
Dependent variable
To model the diversification of nuclear portfolios, we use as our dependent variable the number
of unique nuclear platforms deployed by a state in a given year.ix In choosing this dependent
variable, we echo the substantial literature in economics and finance on diversification in
investment portfolios, in which the number of different assets is commonly used as a proxy for
diversification (Blume and Friend 1975; Goetzmann and Kumar 2008). Of course, this is an
imperfect measure. A state can allocate weapons across each of its nuclear platforms in different
ways, and a mere count of the number of unique weapons systems does not capture this dynamic.
This measure also assumes equivalence between platforms that differ in their underlying
capabilities. A portfolio consisting of a number of different weapons systems with roughly the
same range, yield, and other characteristics is less diversified than a portfolio with the same
number of platforms but wider variation between the capabilities of the platforms.
Still, the number of unique platforms may be the most relevant measure of diversification
available because it comes closest to the actual political process by which nuclear officials and
military planners make changes to nuclear force structure. States must make a conscious
decision to create a new weapons system with a particular set of capabilities dictated by the
18
state’s strategic environment and its domestic constraints. The allocation of weapons across
nuclear platforms, on the other hand, is a function of many factors outside the realm of politics,
such as the technical reliability of the weapons system, deployment conditions, maintenance and
upkeep, and the resulting service life of the platform. In the same way that the ups and downs of
the stock market can quickly cause an investor’s allocation of stocks to slip away from her target,
the distribution of weapons may move independently from the intent of political leaders. A more
reliable measure of an investor’s intended diversification scheme is the portfolio of stocks she
explicitly chooses to buy. While it might be helpful to incorporate into the dependent variable a
measure of the similarity of the different platforms a state employs, reducing the complexities of
platform characteristics into a single index of similarity would inevitably leave out important
dimensions of platform capabilities, biasing the result in ways that are difficult to anticipate.x
Our quantitative analysis employs two different versions of the dependent variable: the
total number of unique nuclear platforms (tactical and strategic) and also the number of unique
strategic platforms.xi We use the strategic portfolio diversity version of the variable to assess the
theories of nuclear force structure that derive from ideas of strategic nuclear deterrence. Existing
studies of nuclear force structure deal almost exclusively with strategic nuclear weapons. Even
the nuclear triad, an important method and framework for the diversification of force structures,
contemplates largely strategic weapons. At the same time, to the extent that force structure
considerations involve the deployment of tactical as well as strategic weapons, omitting tactical
weapons risks biasing our results for those states with substantial tactical weapons portfolios.xii
Explanatory variables
We employ several variables to help understand how domestic constraints affect nuclear force
structure. These variables capture a state’s underlying economic, nuclear, and military capacity.
19
We measure economic strength as the nuclear state’s real GDP in a given year (Gleditsch 2002).
Military resources are reflected in the Correlates of War project’s military expenditure data
(Singer 1988). Because new nuclear platforms often are designed specifically for a particular
nuclear device, the ability of states to develop new warheads may drive platform diversification.
We test this using Jo and Gartzke’s (2007) seven-point composite index of latent nuclear
capacity. We also include as an explanatory variable the total number of nuclear weapons held
by the state in a given year (from the National Resources Defense Council with additions by the
authors). To address the Maturity Hypothesis, we measure nuclear experience by adding one to
the number of years since the state became a nuclear power and taking the log transformation.
Nuclear acquisition dates are those commonly employed in the quantitative literature (Gartzke
and Kroenig 2009).
The Bureaucratic Politics Hypothesis links the bureaucratic strength of an organization to
the decisions of states to diversify their nuclear forces. As a proxy for bureaucratic strength, we
collected data on the proportion of military personnel in the air force and the navy from the IISS
Military Balance and other country-specific sources.xiii We chose the share of military personnel
strength over other measures, such as service budget size, because of the better availability of
these data, because personnel numbers are less subject to measurement error, and because data
on personnel are more responsive to events that alter the bureaucratic environment (such as war).
Turning to the Conventional Deterrence and Opportunity Cost Hypotheses, we measure a
state’s conventional threat environment in three ways. First, we calculate conventional threat by
dividing the sum of rivals’ Composite Index of National Capabilities (CINC) measures by the
state’s CINC score, adding one, and taking the log transformation (Jo and Gartzke 2007; Klein,
Goertz, and Diehl 2006; Singer 1988). Second, we count the number of militarized international
20
disputes in which a state participated over the preceding five years (Ghosn, Palmer, and Bremer
2004). Third, we tally the number of defense pacts to which a state belongs, based on data from
the Correlates of War Project (Gibler and Sarkees 2004). This last measure reflects the fact that
a state with many alliance commitments faces a much more threatening strategic environment—
and possibly different choices about nuclear force structure—than a state with no defense pacts.
Nuclear rivalries may be a major factor driving force structure decisions. To identify
nuclear rivalries, we include a dichotomous variable that takes on the value of one when a rival
has a nuclear weapon (Klein, Goertz, and Diehl 2006). We measure the nuclear capabilities of a
rival as the number of its nuclear weapons and the diversification of its nuclear portfolio.xiv We
test the Rival Distance Hypothesis with the minimum geographic distance between the state and
a nuclear rival (Weidmann, Kuse, and Gleditsch 2010). For states without nuclear rivals, we set
this measure to zero—such states may have less need to project power over a long distance. To
account for the potential for détente to flourish or for a mounting crisis between rivals to derail
cooperation, we also include a count of the number of militarized international disputes a state
has engaged in with its rival in the last five years (Ghosn, Palmer, and Bremer 2004). Finally,
we address the effect of arms control treaties between the United States and Soviet Union with a
dichotomous variable that takes on the value of one for these two states if any of the SALT I,
SALT II, START I, or START II agreements had been signed in the previous two years.
Alliance dynamics are similarly important. We include a dichotomous variable for the
presence of a defense pact with a nuclear state (Gibler and Sarkees 2004)—a commonly used
proxy for a nuclear umbrella. As with nuclear rivals, we measure allied capability with the total
number of nuclear weapons held by allies and the number of unique nuclear platforms they have
21
deployed. We use the minimum geographic distance to a nuclear ally to test the Ally Distance
hypothesis.xv Descriptive statistics for the variables detailed above are shown in Table 2.
[Table 2 about here]
Modeling approach
We employ time-series cross-section data in which the unit of analysis is the country-year. To
address likely serial correlation in our data as well as the fact that we use a count as our outcome
variable, we employ a negative binomial generalized estimating equation (GEE) model with
AR1 working correlation structure (Zorn 2001).xvi Since nuclear platforms cannot be deployed
overnight, we lag our explanatory variables by one year. A one-period lag reflects the
assumption that diversification of nuclear portfolios does not respond immediately to changes in
the domestic constraints or the state’s strategic environment, but also does not require many
years to respond. Here we distinguish between the actual development of new platforms—which
can take many years, even decades in some cases—and the decision to deploy or remove those
platforms, which is likely to be much more responsive to the factors described above.
If the portfolio diversification of one state is related to that of others, as our hypotheses
about nuclear rivals and nuclear allies suggest, then we may have spatial autocorrelation in our
data. We account for this possibility by including in some model specifications explanatory
variables that represent the level of portfolio diversification in rival and allied states. While we
justify these variables above on theoretical grounds, they also serve as spatial lags in our models
and help to correct for the spatial correlation of errors (Beck, Gleditsch, and Beardsley 2006).
While we adopt a pooled model, heterogeneity across states is a concern. It is clear that
the United States and Russia represent a different breed of nuclear weapons state than the other
members of the nuclear club. The two superpowers have many more nuclear weapons than the
22
other nuclear states combined—in 1985, the US and Soviet arsenals accounted for 98 percent of
global nuclear weapons—and a much wider range of strategic interests. Accordingly, we add to
our models a dichotomous variable that takes on a value of one for the United States or Russia.
Cross-time heterogeneity is also a relevant issue. We employ a dichotomous variable that
takes on a value of one for the duration of the Cold War, since different strategic dynamics were
at play prior to 1991. As described above, we also consider accumulated experience with
nuclear weapons using a logged count of the number of years a state has been a nuclear power.
Findings
Results of the negative binomial GEE analyses are shown in Table 3, with robust standard errors
clustered by country. We report eight models in the analysis. The odd-numbered models use the
count of all unique weapons platforms as the dependent variable.xvii Even-numbered models use
the number of unique strategic weapons platforms as the dependent variable. Models 1 and 2
provide a baseline test of factors hypothesized to drive nuclear force structure. Models 3 and 4
examine the effect of nuclear rivalries. Models 5 and 6 look at alliance dynamics, and Models 7
and 8 combine these model specifications. Variables with positive coefficients are associated
with increased nuclear portfolio diversification, while negative coefficients suggest the
opposite.xviii
[Table 3 about here]
The Resource Hypothesis suggests that a lack of economic, military, or nuclear resources
can lead to reduced portfolio diversification. Real GDP, our measure of economic resources, is
negatively associated with portfolio diversification in Models 1 and 3. Oddly, richer states seem
23
less, not more, prone to diversify. The coefficients on military expenditures and nuclear capacity
are positive and significant in most models, while the coefficient for a state’s quantity of nuclear
weapons, another proxy for nuclear capability, is positive and significant in all models. Perhaps
these results should not surprise us. Any state that successfully developed nuclear weapons—a
very expensive proposition—probably has sufficient economic resources to field new nuclear
platforms. Limiting factors are more likely to be the technical hurdles posed by new platforms
and willingness to devote available resources to the task. Clearly, nuclear capacity and weapons
counts are better measures of these factors than a state’s GDP; states with more latent nuclear
capacity and more nuclear weapons tend to field more unique nuclear platforms than other states.
Capacity variables also demonstrate important substantive effects. Using Models 7 and 8
as the basis for calculations, Table 4 reports the average impact on the number of unique nuclear
weapons platforms of increasing the value of a variable from one standard deviation below its
mean to one standard deviation above its mean (or from minimum to maximum for dichotomous
variables). Table 4 only includes variables that are statistically significant at the p<0.10 level.
Moving from a moderately low number of nuclear weapons to a moderately high number, for
example, yields an average increase of about two strategic platforms and about four platforms of
all types, roughly one-third of the mean number of nuclear platforms in each case.
[Table 4 about here]
The Maturity Hypothesis implies that states increase the diversification of their nuclear
portfolios over time. Examination of the time trend for the number of unique nuclear platforms
seems to support this view (see Figure 1). Indeed, nuclear experience has a significant effect on
the decisions of states to deploy new nuclear platforms in all models in the multivariate analysis.
24
After controlling for other factors that drive nuclear force structure, fledgling nuclear states do
appear to have lower levels of portfolio diversification than their more experienced counterparts.
We use data on the percent of military personnel in the air force and navy as a proxy for
the bureaucratic strength of those military branches to better understand the role of bureaucracy
on nuclear force structure. The coefficient on the percentage of air force personnel is positive
and significant in all models, while the navy personnel variable is negative and significant in the
models that include tactical nuclear weapons.xix Despite the apparent contradiction, these results
seem generally consistent with the hypothesis. Nuclear bombers are present in all of the countryyears in our data, so the air force, as the service responsible for the strategic power projection
and control of the airborne nuclear deterrent, is never positioned to oppose the expansion of
nuclear weapons into its sphere. More to the point, strategic bombing is a core mission of air
forces around the globe. There is thus little reason for even highly bureaucratic air forces to
oppose deployment of nuclear weapons on aircraft.
A strong navy, by contrast, may resist the diversification of nuclear portfolios that would
include nuclear weapons at sea. The expansion of nuclear weapons to naval platforms represents
a shift for the navy from its traditional mission, along with a shift in resources from its traditional
procurement emphasis on new naval vessels. This dynamic may be particularly pronounced for
non-strategic naval nuclear weapons, such as anti-submarine helicopters, nuclear torpedoes, and
tactical sea-launched cruise missiles, which represent many more unique platforms and may lack
the prestige and substantial funding increases associated with strategic nuclear weapons systems.
We recognize that manpower strength is far from a perfect proxy for bureaucratic power.
One concern is that measurement error biases our findings. Manpower estimates of Soviet forces
during the Cold War, for example, often were based on counts of military equipment along with
25
assumptions about how many individuals were needed to support particular military capabilities
(Firth and Noren 1998). Given the well-known overestimation of Soviet airpower—the “bomber
gap”—personnel numbers for the Soviet Union in particular may have been systematically overestimated. To assess the sensitivity of our results to such errors, we re-estimated the models after
shifting 50 percent of air force personnel to the navy (and vice versa). Neither change alters our
results.
It is also possible that these measures proxy for overall military capability, rather than for
bureaucratic heft. If modern navies are both leaner and more lethal than their less sophisticated
contemporaries, for example, then our findings could stem from an association between naval
modernization and portfolio diversification, not bureaucracy. There is no obvious correlation in
our data, however, between naval personnel size and the introduction of at least one new naval
capability, the SLBM. All but one state in our dataset saw an increased naval share of military
personnel at the time of its first deployment of an SLBM. While not definitive, this pattern gives
us some reason to doubt that our bureaucratic politics measures are merely proxies for capability.
Our results support the Opportunity Costs Hypothesis. The military disputes variable is
negative and significant in most models, and the coefficient on the count of a state’s alliances is
negative and significant in all models. Rather than spurring the creation of new platforms, as the
Conventional Deterrence Hypothesis predicts, conventional insecurity weakens the impetus to
diversify nuclear portfolios. While conventional deterrence may lead states to invest in
particular types of nuclear forces, conventional threats do not drive overall portfolio
diversification.
Turning to nuclear rivalries, we find some support for the Arms Race Hypothesis: the
number of nuclear weapons deployed by a rival is significantly associated with an increase in
26
diversification. The mere presence of a nuclear rival and the rival’s portfolio diversification,
however, do not affect nuclear force structure. We also find no support for the Rival Distance or
Crisis Hypotheses; measures of rival geographic distance and recent disputes between rivals are
not significant in our tests.xx
Our analysis also casts doubt on the Arms Control Hypothesis. Arms control agreements
seem to have no effect on the number of unique nuclear weapons systems fielded by states. This
finding lends support to arms control critics that see such agreements as emphasizing particular
nuclear forces, without reducing the number or variety of weapons systems overall. It may also
be that the true effect of these agreements occurs too long after signing to be picked up by our
choice of variables. It is conceivable, for example, that the arms control proxies in these models
may be detecting the lingering build-up in nuclear forces that caused the arms control agreements
to be negotiated in the first place, cancelling out any effect from signing the actual agreements.
The presence and rough capabilities of a nuclear ally seem to affect nuclear force
structure decisions. We find limited support for both the Complements and Mirror Image
Hypotheses. The presence of a nuclear ally is associated with a drop in the average number of
unique platforms that a state deploys, in models that include both tactical and strategic weapons
systems. At the same time, the number of nuclear weapons held by allies is associated with an
increase in the number of unique nuclear platforms; states do not appear to free ride off of the
nuclear strength of an ally. A two standard deviation shift in the count of allied nuclear weapons
leads to an average increase of about 2.1 strategic platforms and about 6.3 platforms of all types.
Nuclear alliances, however, do not lead to an exact mirror image of allied force structure;
the number of allied nuclear platforms does not significantly impact the number of platforms a
state holds itself. When it comes to making decisions about a state’s own nuclear force structure,
27
it may be that the number of nuclear weapons an ally possesses is a more salient measure of
nuclear capability than is the overall diversification of its nuclear portfolio.
The minimum geographic distance to a nuclear ally is a statistically significant driver of
reduced portfolio diversification in models that include both tactical and strategic weapons. This
finding runs counter to the expectations of the Ally Distance Hypothesis. The result may reflect
the particular population of states with no nuclear ally; these states receive an allied geographic
distance of zero. When the models are repeated with those states excluded (reducing the sample
from 274 to 128), the coefficient on the minimum distance to an ally becomes positive and
significant.
Superpower status statistically and substantively increased portfolio diversification in all
models. Just being a superpower increased the average number of strategic platforms by about 4,
with 17 additional nuclear platforms of all types. The Cold War had a less pronounced effect on
diversification; the dummy variable did not reach statistical significance in any model.
Conclusion
Decisions about nuclear force structure are complex and interrelated. States must deal with
capacity constraints while responding to international threats, adjusting to rivals’ arsenals, and
coordinating with nuclear allies. Furthermore, decisions about nuclear force structure take place
over multiple dimensions of state interest, and across time. States do not just decide whether a
new nuclear platform brings a needed capability; they also must weigh the diversification of the
portfolio as a whole (both in isolation and in concert with their allies) and evaluate the mix of
particular nuclear asset classes within the portfolio. The determinants of such complex decisions
are themselves complex. Our empirical models suggest that the diversification of nuclear forces
28
is limited by resource constraints and by the need to defend against conventional threats, but that
diversification increases with nuclear experience and the nuclear capabilities of rivals and allies.
This work is an important first step in building a more nuanced understanding of what it
means to be a nuclear power. It is clear that nuclear weapons states are not all the same, and that
difficult decisions about nuclear weapons and international conflict do not end with a state’s first
nuclear test. By highlighting key drivers of nuclear force structure, we hope to initiate a process
where nuclear status is treated less as an on/off switch and more as a continuum of characteristics.
This approach to nuclear security opens the door to new research into ways that nuclear weapons
interact with state attributes and structural factors to influence global peace and security. Factors
like nuclear doctrine, the attributes of nuclear forces, and changes in strategic thinking over time
assume a new importance in this framework, and may be fruitful avenues for future research.
29
Figures and Tables
Table 1: Nuclear Force Structure Hypotheses
Expected Effect
Hypothesis
on Diversification
Domestic
Constraints
Measures
Resources
Increase
Real GDP
Military expenditures
Nuclear capacity index
Number of nuclear weapons
Maturity
Increase
Log of years since becoming a nuclear state
Bureaucratic
Politics
Bureaucratic politics
Decrease
Air force personnel (percent of military)
Navy personnel (percent of military)
Conventional
Threats
Conventional deterrence
Increase
Opportunity costs
Decrease
Conventional threats
Disputes over previous 5 years
Number of defense pacts
Arms race
Increase
Nuclear rival
Rivals’ number of nuclear weapons
Rivals’ number of unique platforms
Rival distance
Increase
Minimum geographic distance to a nuclear rival
Crisis
Increase
Disputes with rival over previous 5 years
Arms control
Decrease
Arms control agreement signed within 2 years
Complements
Decrease
Mirror image
Increase
Defense pact with nuclear state
Allies’ number of nuclear weapons
Allies’ number of unique platforms
Ally distance
Increase
Nuclear
Rivalries
Nuclear
Alliances
Minimum geographic distance to a nuclear ally
30
Table 2: Descriptive Statistics
Variable
Mean
Number of strategic nuclear platforms
Number of nuclear platforms
11.16
6.11
Domestic Constraints GDP
Military expenditures
Nuclear capacity
Number of nuclear weapons
Nuclear experience
Bureaucracy
Standard
Deviation
Minimum
Maximum
13.16
3.89
1.00
1.00
57.00
18.00
1.68
0.55
6.88
0.65
2.82
1.83
0.78
0.42
1.09
0.91
0.04
0.01
5.00
0.00
0.00
9.41
3.18
7.00
4.07
4.01
Air force personnel (%)
Navy personnel (%)
0.20
0.15
0.09
0.09
0.03
0.03
0.36
0.33
Conventional Threat
Conventional threat
Disputes (last five years)
Number of defense pacts
1.28
14.51
14.08
0.76
9.29
15.64
0.00
0.00
0.00
4.41
38.00
53.00
Nuclear Rivalries
Nuclear rival
Rivals' number of nuclear weapons
Rivals' portfolio diversification
Rival's strategic portfolio diversification
Distance to rival
Disputes with nuclear rival (last five years)
Arms control agreements
0.74
1.55
23.51
9.88
0.03
4.71
0.08
0.44
1.69
22.29
8.35
0.08
6.21
0.27
0.00
0.00
0.00
0.00
0.00
0.00
0.00
1.00
6.40
69.00
25.00
0.82
26.00
1.00
Nuclear Alliances
Defense pact with nuclear state
Allies' number of nuclear weapons
Allies' portfolio diversification
Allies' strategic portfolio diversification
Distance to ally
0.47
0.68
7.07
5.20
0.07
0.50
1.09
8.48
6.48
0.16
0.00
0.00
0.00
0.00
0.00
1.00
3.20
25.00
21.00
0.41
US or Russia
Cold War
0.35
0.77
0.48
0.42
0.00
0.00
1.00
1.00
Dependent Variable
31
Table 3: Analysis of Number of Unique Nuclear Platforms
Model 1
All Platforms
Domestic Constraints GDP
Military expenditures
Nuclear capacity
Number of nuclear weapons
Nuclear experience
-0.025
0.056
0.191
0.238
0.191
Bureaucracy
Air force personnel (%)
Navy personnel (%)
1.038 (0.420) *
-0.631 (0.227) **
Conventional Threat
Conventional threat
Disputes (last five years)
Number of defense pacts
0.000 (0.040)
0.020 (0.035)
-0.007 (0.001) *** -0.007 (0.004) ^
-0.005 (0.002) *
-0.010 (0.003) **
Nuclear Rivalries
Nuclear rival
Rivals' number of nuclear weapons
Rivals' portfolio diversification
Rival's strategic portfolio diversification
Distance to rival
Disputes with nuclear rival (last five years)
Arms control agreements
-0.076 (0.074)
Defense pact with nuclear state
Allies' number of nuclear weapons
Allies' portfolio diversification
Allies' strategic portfolio diversification
Distance to ally
-0.096 (0.020) *** -0.050 (0.033)
Nuclear Alliances
US or Russia
Cold War
Constant
N
(0.008)
(0.016)
(0.057)
(0.047)
(0.071)
Model 2
Strategic Platforms
Model 3
All Platforms
** -0.008 (0.019)
-0.036 (0.015) *
-0.010 (0.022)
*** 0.016 (0.010) ^
0.042 (0.012) *** 0.007 (0.011)
*** 0.160 (0.122)
0.192 (0.070) **
0.146 (0.116)
*** 0.169 (0.047) *** 0.226 (0.033) *** 0.168 (0.037) ***
**
0.218 (0.084) **
0.162 (0.062) **
0.203 (0.083) *
0.653 (0.259) *
-0.299 (0.433)
0.864 (0.369) *
-0.473 (0.193) *
0.000 (0.006)
0.010 (0.019)
1.113 (0.481) *
0.009 (0.038)
274
0.651 (0.279) *
-0.159 (0.503)
-0.057 (0.058)
-0.024 (0.041)
-0.007 (0.002) *** -0.007 (0.004)
-0.008 (0.003) ** -0.011 (0.005) *
-0.113 (0.105)
0.111 (0.060) ^
-0.003 (0.003)
-0.269 (0.427)
Model 4
Strategic Platforms
-0.003 (0.006)
0.001 (0.030)
0.581 (0.248) *
0.021 (0.053)
-0.138 (0.775)
274
0.058 (0.034) ^
-0.109 (0.224)
0.000 (0.006)
0.009 (0.020)
-0.005
-0.091
-0.004
0.003
-0.073 (0.025) **
-0.038 (0.036)
1.389 (0.455) **
-0.020 (0.044)
-0.300 (0.567)
274
(0.007)
(0.122)
(0.006)
(0.026)
0.562 (0.237) *
0.003 (0.051)
-0.046 (0.767)
274
GEE negative binomial coefficients with robust standard errors, clustered by country, in parentheses. An AR1 working correlation structure is used.
Explanatory variables are lagged one year.
*** p<0.001, ** p<0.01, * p<0.05, ^ p<0.10
32
Table 3: Analysis of Number of Unique Nuclear Platforms (Continued)
Model 5
All Platforms
Bureaucracy
Air force personnel (%)
Navy personnel (%)
0.608 (0.191) **
0.471 (0.235) *
-0.920 (0.227) *** -0.476 (0.409)
0.519 (0.181) **
0.458 (0.263) ^
-0.802 (0.206) *** -0.343 (0.487)
Conventional Threat
Conventional threat
Disputes (last five years)
Number of defense pacts
-0.040 (0.040)
-0.005 (0.035)
-0.007 (0.002) *** -0.007 (0.004)
-0.020 (0.005) *** -0.014 (0.004) **
-0.055 (0.054)
-0.043 (0.035)
-0.008 (0.003) ** -0.007 (0.005)
-0.020 (0.005) *** -0.014 (0.005) **
Nuclear Rivalries
Nuclear rival
Rivals' number of nuclear weapons
Rivals' portfolio diversification
Rival's strategic portfolio diversification
Distance to rival
Disputes with nuclear rival (last five years)
Arms control agreements
Defense pact with nuclear state
Allies' number of nuclear weapons
Allies' portfolio diversification
Allies' strategic portfolio diversification
Distance to ally
US or Russia
Cold War
Constant
N
0.002 (0.088)
(0.028)
(0.007)
(0.096)
(0.044)
(0.086)
*
*
***
*
-0.022
0.050
0.205
0.236
0.149
(0.035)
(0.013)
(0.076)
(0.009)
(0.068)
Model 8
Strategic Platforms
-0.024
0.054
0.226
0.237
0.194
**
**
***
*
0.008
0.017
0.231
0.176
0.196
Model 7
All Platforms
Domestic Constraints GDP
Military expenditures
Nuclear capacity
Number of nuclear weapons
Nuclear experience
Nuclear Alliances
(0.028)
(0.021)
(0.073)
(0.019)
(0.079)
Model 6
Strategic Platforms
***
**
***
*
0.320 (0.066) ***
-0.004 (0.006)
-0.497 (0.190) **
1.586 (0.170) ***
0.039 (0.032)
-0.540 (0.483)
274
(0.032)
(0.009)
(0.092) *
(0.034) ***
(0.083) *
-0.085 (0.111)
0.158 (0.060) **
-0.006 (0.004)
0.004 (0.006)
0.009 (0.026)
0.008
0.008
0.232
0.178
0.180
-0.002 (0.006)
0.006 (0.028)
0.155 (0.090) ^
-0.003 (0.002)
-0.044 (0.091)
-0.215 (0.247)
0.005 (0.005)
0.012 (0.026)
0.377 (0.075) ***
-0.005 (0.007)
-0.401 (0.158) *
0.065 (0.034) ^
-0.006
-0.094
-0.003
0.008
(0.008)
(0.112)
(0.006)
(0.024)
0.177 (0.085) *
-0.005 (0.003)
-0.002 (0.118)
0.737 (0.183) *** 1.608 (0.150) *** 0.722 (0.147) ***
0.010 (0.050)
-0.019 (0.029)
-0.015 (0.046)
-0.617 (0.624)
274
-0.332 (0.504)
274
-0.614 (0.626)
274
GEE negative binomial coefficients with robust standard errors, clustered by country, in parentheses. An AR1 working correlation structure is used.
Explanatory variables are lagged one year.
*** p<0.001, ** p<0.01, * p<0.05, ^ p<0.10
33
Table 4: Substantive Effects of Statistically Significant Variables
Model 7
All Platforms
Model 8
Strategic Platforms
Domestic Constraints Military expenditures
Nuclear capacity
Number of nuclear weapons
Nuclear experience
0.58
1.28
3.89
2.04
1.02
2.07
1.74
Bureaucracy
Air force personnel (%)
Navy personnel (%)
0.67
-1.02
Conventional Threat
Disputes (last five years)
Number of defense pacts
-1.12
-4.81
-2.41
Nuclear Rivalries
Rivals' number of nuclear weapons
4.05
1.17
Nuclear Alliances
Allies' number of nuclear weapons
Distance to ally
6.34
-0.94
2.07
US or Russia
17.10
4.36
0.42
The average change in the number of unique nuclear platforms when the variable is increased from
one standard deviation below its mean to one standard deviation above its mean (for continuous
variables) or from its minimum to its maximum (for dichotomous variables). Values are included
only for variables that were statistically significant at the p<0.10 level for the model in question.
See Table 2 for descriptive statistics for each of these variables.
34
10
20
30
40
All nuclear states
States with aircraft, missiles, and SLBMs
States with aircraft and missiles only
States with aircraft only
0
Mean Number of Unique Platforms
Figure 1: Unique Nuclear Platforms Over Time
0
10
20
30
40
50
Years with Nuclear Weapons
35
References
Allison, Graham T. and Frederic A. Morris. 1975. “Armaments and Arms Control: Exploring the
Determinants of Military Weapons.” Daedalus. 104(3): 99-129.
Asal, Victor, and Kyle Beardsley. 2007. “Proliferation and International Crisis Behavior.”
Journal of Peace Research 44(2): 139–155.
Barkley, Daniel. 2008. “Ballistic Missile Proliferation An Empirical Investigation.” Journal of
Conflict Resolution 52(3): 455–473.
Bas, Muhammet A. and Andrew J. Coe. 2012. “Arms Diffusion and War.” Journal of Conflict
Resolution 56(4): 651–674.
Beardsley, Kyle and Victor Asal. 2009. “Winning with the Bomb.” Journal of Conflict
Resolution 53(2): 278–301.
Beck, Nathaniel, Kristian Skrede Gleditsch, and Kyle Beardsley. 2006. “Space Is More than
Geography: Using Spatial Econometrics in the Study of Political Economy, Space Is More
than Geography: Using Spatial Econometrics in the Study of Political Economy.”
International Studies Quarterly 50(1): 27–44.
Bleek, Philipp and Eric Lorber. This Issue. “Security Guarantees and Allied Nuclear
Proliferation.”
Blume, Marshall E., and Irwin Friend. 1975. “The Asset Structure of Individual Portfolios and
Some Implications for Utility Functions.” The Journal of Finance 30(2): 585–603.
36
Brown, Robert L. and Jeffrey M. Kaplow. This issue. “Talking Peace, Making Weapons: IAEA
Technical Cooperation and Nuclear Proliferation.”
Burt, Richard. 1978. “Reducing strategic arms at SALT: How difficult, how important?” The
Adelphi Papers 18(141): 4–14.
Chari, P. R. 2001. "Nuclear Restraint, Nuclear Risk Reduction, and the Security-Insecurity
Paradox in South Asia." The Henry L. Stimson Center.
Chyba, Christopher F., and J. D. Crouch. 2009. “Understanding the U.S. Nuclear Weapons
Policy Debate.” The Washington Quarterly 32(3): 21–36.
Cochran, Thomas B et al. 1989. Nuclear Weapons Databook, Volume IV: Soviet Nuclear
Weapons. New York, NY: Harper & Row, Ballinger.
Cochran, Thomas B, William M Arkin, and Milton M Hoenig. 1984. Nuclear Weapons
Databook, Volume I: U.S. Nuclear Forces and Capabilities. Cambridge, Mass.: Ballinger
Pub. Co.
Collina, Tom Z., and Daryl G. Kimbal. 2010. Now More Than Ever: The Case for the
Comprehensive Nuclear Test Ban Treaty. Arms Control Association.
Collins, John M. 1981. "Triage of Triads." Fletcher F. 5: 362.
Cortright, David., and Raimo Väyrynen. 2010. Towards nuclear zero. London: Routledge.
Enthoven, Alain C., and K. Wayne Smith. 1971. How Much is Enough?: Shaping the Defense
Program, 1961-1969. Rand Corporation.
37
Eyre, D. P. and M. C. Suchman. 1996. “Status, norms, and the proliferation of conventional
weapons: An institutional theory approach.” The Culture of National Security: 79–113.
Firth, Noel E. and James H. Noren. 1998. Soviet Defense Spending: A History of CIA Estimates,
1950-1990. College Station, TX: Texas A&M University Press.
Flory, Peter C.W. 2006. “Nuclear Exchange: Does Washington Really Have (or Want) Nuclear
Primacy - Just the Facts.” Foreign Affairs 85(5): 149–150.
Fuhrmann, Matthew. 2009. “Spreading Temptation: Proliferation and Peaceful Nuclear
Cooperation Agreements.” International Security 34(1): 7–41.
Gartzke, Erik, and Dong-Joon Jo. 2009. “Bargaining, Nuclear Proliferation, and Interstate
Disputes.” Journal of Conflict Resolution 53(2): 209–233.
Gartzke, Erik, and Matthew Kroenig. 2009. “A Strategic Approach to Nuclear Proliferation.”
Journal of Conflict Resolution 53(2): 151–160.
Gartzke, Erik and Matthew Kroenig. This issue. “Nuclear Posture, Nonproliferation Policy, and
the Spread of Nuclear Weapons.”
Ghosn, Faten, Glenn Palmer, and Stuart A. Bremer. 2004. “The MID3 Data Set, 1993–2001:
Procedures, Coding Rules, and Description.” Conflict Management and Peace Science
21(2): 133–154.
Gibler, Douglas M, and Meredith Reid Sarkees. 2004. “Measuring Alliances: The Correlates of
War Formal Interstate Alliance Dataset, 1816–2000.” Journal of Peace Research 41(2):
211–222.
38
Gleditsch, Kristian Skrede. 2002. “Expanded Trade and GDP Data.” Journal of Conflict
Resolution 46(5): 712–724.
Goetzmann, William N., and Alok Kumar. 2008. “Equity Portfolio Diversification.” Review of
Finance 12(3): 433–463.
Halperin, Morton 1974. Bureaucratic Politics and Foreign Policy. Washington, DC: Brookings
Institution.
Heckman, James J. 1976. “The Common Structure of Statistical Models of Truncation, Sample
Selection and Limited Dependent Variables and a Simple Estimator for Such Models.”
Annals of Economic and Social Measurement 5(4): 475-492.
Horowitz, Michael. 2009. “The Spread of Nuclear Weapons and International Conflict: Does
Experience Matter?” Journal of Conflict Resolution 53(2): 234–257.
Horowitz, Michael and Neil Narang. This Issue. “Are Nuclear, Biological, and Chemical
Weapons Substitutes? Comparing the Determinants of WMD Proliferation.”
International Institute for Strategic Studies. 1963-. The Military Balance. London: International
Institute for Strategic Studies.
Jo, Dong-Joon, and Erik Gartzke. 2007. “Determinants of Nuclear Weapons Proliferation.”
Journal of Conflict Resolution 51(1): 167–194.
Kak, Kapil. 1998. "Command and Control of Small Nuclear Arsenals." Nuclear India: 268.
Klein, James P, Gary Goertz, and Paul F Diehl. 2006. “The New Rivalry Dataset: Procedures and
Patterns.” Journal of Peace Research 43(3): 331–348.
39
Kristensen, Hans. 2012. Non-Strategic Nuclear Weapons. Federation of American Scientists.
Special Report.
Kroenig, Matthew. 2009. “Importing the Bomb: Sensitive Nuclear Assistance and Nuclear
Proliferation.” Journal of Conflict Resolution 53(2): 161–180.
Kugler, Jacek, Abramo Fimo Kenneth Organski, and Daniel J. Fox. 1980. "Deterrence and the
Arms Race: The Impotence of Power." International Security: 105-138.
Lebow, Richard Ned, and Janice Gross Stein. 1995. "Deterrence and the Cold War." Political
Science Quarterly 110.2: 157-181.
Lieber, Keir A., and Daryl G. Press. 2009. “The Nukes We Need: Preserving the American
Deterrent.” Foreign Affairs 88: 39.
———. 2006. “The Rise of US Nuclear Primacy.” Foreign Affairs 85: 42.
McCarthy, John F. 1976. “The Case for the B-1 Bomber.” International Security 1(2): 78–97.
Mettler, Simon A., and Dan Reiter. 2012. “Ballistic Missiles and International Conflict.” Journal
of Conflict Resolution.
Millar, Alistair, and Brian Alexander. 2003. Tactical Nuclear Weapons: Emergent Threats in an
Evolving Security Environment. New York: Brassey’s.
Narang, Vipin. 2010. “Posturing for Peace? Pakistan’s Nuclear Postures and South Asian
Stability.” International Security 34(3): 38–78.
40
Norris, Robert S, Andrew S Burrows, and Richard W Fieldhouse. 1994. Nuclear Weapons
Databook, Volume V: British, French, and Chinese Nuclear Weapons. Boulder, CO:
Westview Press.
Payne, Keith. 2006. “Nuclear Exchange: Does Washington Really Have (or Want) Nuclear
Primacy - A Matter of Record.” Foreign Affairs 85(5): 150–152.
Perrow, Charles. 1986. "Economic Theories of Organization." Theory and society, 15(1), 11-45.
Pifer, Steven. 2010. “New START: Good News for US Security.” Arms Control Today 40(4): 8–
14.
Richardson, Lewis Fry. 1960. Arms and Insecurity: A Mathematical Study of the Causes and
Origins of War. Boxwood Press.
Rosen, Stephen P. 1991. Winning the next war: Innovation and the modern military. Ithaca, NY:
Cornell University Press.
Sagan, Scott Douglas, and Arwen Mohun. 1993. The Limits of Safety: Organizations, Accidents,
and Nuclear Weapons. Princeton, NJ: Princeton University Press.
Sagan, Scott D. 1994. "The Perils of Proliferation: Organization Theory, Deterrence Theory, and
the Spread of Nuclear Weapons. International Security, 66-107.
Sagan, Scott D. 1996. “Why Do States Build Nuclear Weapons?: Three Models in Search of a
Bomb.” International Security 21(3): 54–86.
Sagan, Scott D., and Kenneth N. Waltz. 1995. The Spread of Nuclear Weapons: A debate. New
York: W.W. Norton.
41
Sapolsky, Harvey. 1972. The Polaris System Development. Cambridge, Mass.: Harvard
University Press.
Sechser, Todd S. and Matthew Fuhrmann. This issue. “Nuclear Strategy, Nonproliferation, and
the Causes of Foreign Nuclear Deployments.”
Sechser, Todd S. and Elizabeth N. Saunders. 2010. “The Army You Have: The Determinants of
Military Mechanization, 1979–2001.” International Studies Quarterly 54(2): 481–511.
Singer, J. David. 1988. “Reconstructing the correlates of war dataset on material capabilities of
states, 1816–1985.” International Interactions 14(2): 115–132.
Singh, Sonali and Christopher R. Way. 2004. “The Correlates of Nuclear Proliferation: A
Quantitative Test.” Journal of Conflict Resolution 48(6): 859–885.
Snow, Donald M. 1979. “Current Nuclear Deterrence Thinking: An Overview and Review.”
International Studies Quarterly 23(3): 445–486.
Solingen, Etel. 1994. “The Political Economy of Nuclear Restraint.” International Security
19(2): 126–169.
Stockholm International Peace Research Institute. 1968-. Annual Yearbook. London, England:
Oxford University Press.
Tago, Atsushi and J. David Singer. 2011. “Predicting the Horizontal Proliferation of Nuclear
Weapons.” Kobe University Law Review (45): 51–68.
United States Air Force. 1945-. USAF Statistical Digests and Summaries.
http://www.afhso.af.mil/usafstatistics/ (Accessed July 1, 2013).
42
United States Department of Defense. 2010. Nuclear Posture Review Report.
———. 2002. Nuclear Posture Review Report: Foreword.
http://www.defense.gov/news/jan2002/d20020109npr.pdf (Accessed April 12, 2012).
Waltz, Kenneth N. 1990. “Nuclear Myths and Political Realities.” American Political Science
Review, 84 (3): 731-745.
Weidmann, Nils B., Doreen Kuse, and Kristian Skrede Gleditsch. 2010. “The Geography of the
International System: The CShapes Dataset.” International Interactions 36(1): 86–106.
Younger, Stephen. 2000. “Nuclear Weapons in the Twenty-First Century.” Los Alamos National
Laboratory.
Zorn, Christopher J. W. 2001. “Generalized Estimating Equation Models for Correlated Data: A
Review with Applications.” American Journal of Political Science 45(2): 470–490.
43
Notes
i
Analysts use varying definitions of nuclear force structure, including everything from simple weapons counts to the
entire command, control, and intelligence infrastructure behind these weapons. We see nuclear force structure
broadly as describing the quality, quantity, and type of nuclear weapons and delivery platforms deployed by a state.
At the same time, this definition excludes questions of nuclear doctrine and the larger national security apparatus.
ii
Nuclear platforms are a means for delivering nuclear weapons, including aircraft and missiles (submarine-launched
or land-based). We use the terms “nuclear platform,” “delivery vehicle,” and “weapons system” interchangeably.
iii
The three legs of the nuclear triad are generally seen to include strategic bombers, intercontinental ballistic
missiles, and submarine-launched ballistic missiles. Other, more esoteric, formulations exist: The US 2002 Nuclear
Posture Review advances the idea of a “new triad” that consists of nuclear and non-nuclear offensive strike systems,
active and passive defenses, and an enhanced defense infrastructure (U.S. Department of Defense 2002). Here, we
take the components of the nuclear triad to mean strategic air, land, and sea-based weapons of all ranges and
capabilities.
iv
Horowitz (2009) conducts robustness checks using variables meant to represent nuclear force structure—the
number of nuclear weapons held by the state and whether it has deployed land-based missiles or SLBMs—but he
does not report whether these force structure variables are significantly associated with the likelihood of conflict.
v
Our dataset includes deployed nuclear platforms for the United States (1950-2000), the Soviet Union/Russia
(1956-2000), the United Kingdom (1961-2000), France (1961-2000), China (1964-2000), Israel (1972-2000), South
Africa (1982-1990), India (1988-2000), and Pakistan (1990-2000). In several cases states deployed nuclear weapons
before coverage begins in our dataset. Reliable nuclear platform information was only available for the dates listed.
vi
Please see the data appendix for a description of our data collection efforts and a complete list of sources used.
vii
Our data on nuclear platforms include aircraft, land-based missiles, and submarine-launched missiles. We
exclude nuclear gravity-type bombs and air-launched missiles, and count all nuclear artillery as a single platform.
viii
The trend line representing nuclear triad states ultimately merges with the trend line for all nuclear states; the only
states with 50 years of nuclear experience (the United States and Russia) have the nuclear triad.
44
ix
Platforms need not be associated with different legs of the nuclear triad to be considered unique. For example, the
US B1-B and the B2 bombers, though both aircraft, are treated as unique platforms. Variants of existing platforms
are not treated as unique unless they have substantially different capabilities. We defer to source material as to
whether delivery vehicles really represent different platforms. Please see the data appendix for more information.
x
We examine the diversity of nuclear portfolios in this paper as a first step toward understanding the determinants
of nuclear force structure. A complementary approach might examine the factors that lead states to deploy weapons
with specific capabilities. We leave that effort for future research.
xi
These measures are identical for Israel, South Africa, India, and Pakistan. All weapons systems in these states are
considered strategic, both by our data sources and the states themselves. There is some debate about whether China
has deployed non-strategic weapons; our primary models assume it has not, but we relax this assumption in
robustness checks.
xii
There exists no clear criteria by which to distinguish between strategic and tactical (also known as theater or non-
strategic) weapons systems (Kristensen 2012; Millar and Alexander 2003). We rely on our sources to best capture
the prevailing view of analysts about particular weapons systems. Please see the data appendix for additional detail.
xiii
Missing values were imputed where data were available for some country-years but not others.
xiv
When the dependent variable is limited to strategic nuclear weapons, the rival diversification variable counts only
unique strategic platforms deployed by the rival. The variable equals zero in the absence of a nuclear rival.
xv
As with the nuclear rival measure, tactical platforms are included in the ally diversification measure when tactical
platforms also are included in the dependent variable. These variables are set to zero in the absence of a nuclear ally.
xvi
We use Stata’s xtgee command to estimate all models. In each case, we capture the α dispersion parameter from
a standard negative binomial model and use that parameter for the negative binomial GEE. The negative binomial
model reduces to a poisson when α is zero. In no case was α significantly different from zero, suggesting a poisson
model would also be suitable. Model convergence issues prevented using a poisson GEE for each model, but results
were nearly identical in those cases where both poisson GEE and negative binomial GEE models could be estimated.
xvii
The models shown in Table 3 assume that China has not deployed tactical nuclear weapons, but analysts disagree
as to whether this is so. We tested the sensitivity of this assumption for our results by adding arbitrary numbers of
Chinese tactical weapons systems and re-estimating the models. Although these tests do lead to some changes to the
45
substantive and statistical significance of a few variables, they do not affect overall conclusions with respect to our
hypotheses. Doubling China’s platform count, for example, does not alter any results for Models 7 and 8.
xviii
Countries with nuclear weapons have obviously experienced a previous stage of proliferation before choosing
policies to develop particular force structures. Selection into nuclear status could be a source of concern.
Phenomena like salary differential between genders are underestimated when differential incomes cause less skilled
women to refrain from entering the job market (Heckman 1976). Three factors are worth considering here. First,
force structure differs from income in that few countries proliferate (compared to the percentage of adults in the
workforce) and one is consumption and the other compensation. We find it difficult to imagine that countries would
proliferate if they could have eight nuclear weapons platforms, for example, but would stay in the non-nuclear club
if they could only develop seven platforms. Second, and possibly more important, the likely result of this type of
bias is to underestimate the effects reported here. By not modeling selection into nuclear status, we are reducing the
likely range of values on key independent variables, to the degree that these variables also predict nuclear status.
This is of course exactly the problem for Heckman in estimating wage differentials. Again, in the context of
hypotheses about nuclear security, we may be less concerned about measuring the magnitude of effects than about
being conservative in accepting hypothetical claims. Finally, and not unimportantly, modeling a two stage selection
process in the context of our estimator is highly problematic. We do not attempt this approach here.
xix
We conducted a number of robustness checks on these variables. Making reasonable adjustments to the imputed
values, but not dropping imputed observations, does not change our results. However, excluding imputed values,
which drops a total of 11 country-years from the analysis, causes the air force variable to lose statistical significance
in Models 2 and 4 through 8. Conversely, the navy variable gains statistical significance in Model 6. Excluding the
bureaucratic politics variables altogether does not substantially alter our findings for any of the other hypotheses.
xx
Because there may be some overlap in the various rival measures, we re-estimated the models while including
only one rival measure at a time. This does not affect the results.
46